Naturally, the most reliable results have been obtained for the two-leg ladder, \(W=2\) . So long as \(x < x_c \sim 0.3\) , for the typical range of intermediate \(U\)  and \(t^{\prime }/t\) , there is general consensus [1]}, [2]}, [3]}, [4]} that, in the \(L\rightarrow \infty \)  limit, such ladders generically form a Luther-Emery liquid.= [5]}. Specifically, there is a non-zero spin-gap, \(\Delta _{\rm s} \sim t^2/U\) , a single gapless charge mode (\(c=1\) ) and power-law equal-time CDW and SC correlations which fall as \(\cos (Q^{\vphantom{\dagger }}_{\rm CDW}r + \phi _0)|r|^{-K^{\vphantom{\dagger }}_{\rm CDW}}\)  and \(|r|^{-K^{\vphantom{\dagger }}_{\rm SC}}\) , respectively. The CDW ordering vector is equal to the value of \(2k^{\vphantom{\dagger }}_{\rm F}=W\pi n\)  mandated by the generalized LSM theorem (see § ), \(Q^{\vphantom{\dagger }}_{\rm CDW}=W\pi n\equiv 2\pi x\)  and consistent with expectations from conformal field theory, \(K^{\vphantom{\dagger }}_{\rm SC} = 1/K^{\vphantom{\dagger }}_{\rm CDW}\) .
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